PRP Records

Probable Primes Top 10000

(295149 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
90012^335222-109985100912Enzo Doria04/2014
90022^335182-17237100900Enzo Doria05/2013
9003(2^335107+1634)/2100877Stefano Morozzi09/2020
90042^335043-16737100858Enzo Doria05/2013
9005(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
90062^335038-20633100857Enzo Doria06/2013
90072^335031+1873373100855Enzo Doria06/2016
900823489^19650+19650^23489100847Hans Havermann10/2018
90093^211354-8816100842Enzo Doria05/2014
90102^334984-112757100841Enzo Doria06/2014
9011(746*10^100827+1)/9100829Robert Price03/2020
901229451^2648+2648^29451100809Hans Havermann09/2018
901325583^8716+8716^25583100806Hans Havermann08/2018
90152^334857+48527100803Lelio R Paula08/2011
901412^93406+29100803Lelio R Paula10/2016
901628780^3179+3179^28780100796Hans Havermann09/2018
9017(5*2^334825+1)/47100792Lelio R Paula12/2013
9018(328^40063-1)/327100791Serge Batalov06/2022
90192^334809-13100788Lelio R Paula04/2011
9020(3552^28387-1)/3551100784Serge Batalov06/2022
9021(82*10^100780-1)/9100781Robert Price12/2014
902231395^1622+1622^31395100780Hans Havermann09/2018
9023(2^334779+47)/5100778Lelio R Paula12/2013
90242^334751+2049100771Lelio R Paula09/2016
902513^90443-98100749Lelio R Paula10/2016
9026(2^334674+3190)/2100747Stefano Morozzi09/2020
9027(2^334651+1050)/2100740Stefano Morozzi09/2020
9028(7*10^100737+71)/3100738Robert Price05/2018
9029(24737*2^334628+1)/3100737Lelio R Paula07/2014
903015^85639-28100720Lelio R Paula10/2016
903127068^5259+5259^27068100718Hans Havermann08/2018
90322^334562+577294575100711Lelio R Paula09/2016
90334*3^211077-5100710Lelio R Paula08/2014
90342^334524+145100702Lelio R Paula07/2009
9035(2^334451+714)/2100680Stefano Morozzi09/2020
903627648^4375+4375^27648100666Hans Havermann09/2018
9037(1017*2^334391-1)/3535100662Lelio R Paula05/2015
9038(2^334309+3122)/2100637Stefano Morozzi09/2020
90392^334294-113111100633Enzo Doria07/2014
904025581^8582+8582^25581100626Hans Havermann08/2018
90426^129308-17723100622Enzo Doria03/2013
9041(19*10^100627+287)/9/292157100622Alfred Reich11/2022
90436^129305+95100619Lelio R Paula10/2016
90442^334244-1167100618Lelio R Paula09/2016
9045(2^334233+3066)/2100614Stefano Morozzi09/2020
9046(76*10^100611+77)/9100612Robert Price10/2019
90477*10^100606-93100607Robert Price08/2020
9048(26*10^100566+49)/3100567Robert Price08/2019
9049(21*2^334050+1)/935100558Lelio R Paula12/2013
905024885^10984+10984^24885100555Hans Havermann07/2018
9051(1351^32119-1)/1350100551Serge Batalov06/2022
9052(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
9053(35*10^100542+1)/9100543Serge Batalov11/2010
905423578^18367+18367^23578100538Hans Havermann07/2018
905513^90251+24100535Lelio R Paula10/2016
90562^333963+789100533Lelio R Paula08/2011
90572^333919-1840087100520Enzo Doria06/2015
9058(2^333916+1698)/2100519Stefano Morozzi09/2020
90592^333911+72623100518Enzo Doria04/2016
906024605^12168+12168^24605100517Hans Havermann08/2018
906166*10^100502+7100504Robert Price07/2020
906218^80064-67100503Lelio R Paula10/2016
9063(13*10^100487+137)/3100488Robert Price06/2021
906423034^23034-12085^12085100483Serge Batalov04/2024
90655^143742-48100472Lelio R Paula10/2016
906624095^14784+14784^24095100472Hans Havermann08/2018
90672^333757-112123100471Enzo Doria06/2014
9068(7953^25759-1)/7952100470Serge Batalov06/2022
906923030^23030-7401^7401100464Serge Batalov04/2024
90707*10^100457-57100458Robert Price06/2020
907127358^4693+4693^27358100444Hans Havermann07/2018
90728*10^100439-51100440Robert Price08/2019
90732^333603-108861100425Enzo Doria03/2014
90749*7^118818-2100414Lelio R Paula11/2014
90752^333546-17097100408Enzo Doria05/2013
9076(19*10^100403+287)/9/3100403Alfred Reich11/2022
907717^81597+72100401Lelio R Paula10/2016
9078(3613^28219-1)/3612100396Serge Batalov06/2022
9079p(20559)#/2+8100384Robert Price01/2017
908011^96390-24100380Lelio R Paula10/2016
908123011^23011+18846^18846100373Serge Batalov04/2024
9082(2^333385+2730)/2100359Stefano Morozzi09/2020
90834832563059*2^333333+30029100353Donovan Johnson01/2008
908423565^18136+18136^23565100353Hans Havermann07/2018
90852^333354+763100350Lelio R Paula08/2011
9086(1608961*2^333333+1)/3100349Alex_soldier09/2022
9087(424517*2^333333+1)/5100349Alex_soldier09/2022
9088(887087*2^333333+1)/5100349Alex_soldier09/2022
9089(1159703*2^333333+1)/7100349Alex_soldier09/2022
9090(25*10^100343-67)/3100344Robert Price06/2019
90912^333289-109483100330Enzo Doria04/2014
90922^333240-2790209100316Enzo Doria03/2016
909323601^17798+17798^23601100314Hans Havermann05/2018
9095(2^333227-2^166614+1)/510031111/2006
90942^333225+719100311Lelio R Paula08/2011
90962^333221-2785333100310Enzo Doria10/2015
909776^53332-75100308Norbert Schneider02/2015
9098(29*10^100302+583)/9100303Robert Price06/2021
90996^128892-17573100298Enzo Doria03/2013
9100(47*10^100283-119)/9100284Robert Price05/2019
91012^333105-113215100275Enzo Doria07/2014
9102(31*2^333102+1)/2375100272Lelio R Paula11/2013
91034*10^100257-83100258Robert Price10/2018
910417^81476-74100253Lelio R Paula10/2016
910523392^19207+19207^23392100199Hans Havermann06/2018
9106(2^332830+750)/2100192Stefano Morozzi09/2020
9107(206*10^100189-17)/9100191Robert Price01/2020
910817^81417-16100180Theodore Burton11/2005
9109(2^332773+590)/2100175Stefano Morozzi09/2020
91102*23^73562+215100172Eric Chen08/2023
91122^332739-113215100165Enzo Doria07/2014
9111(19*31^67163-199)/30100165Eric Chen04/2024
91132^332730-1865621100162Enzo Doria03/2016
911491^51127-2100160Lelio R Paula09/2013
911515^85159-32100155Lelio R Paula10/2016
911622963^22963+4620^4620100143Serge Batalov04/2024
911722960^22960+9991^9991100128Serge Batalov04/2024
91186^128661+97100118Lelio R Paula10/2016
911919^78285+40100108Lelio R Paula07/2016
91206^128640+5100102Lelio R Paula11/2014
912110^100095+89973100096Patrick De Geest10/2022
912210^100095-400001100095Robert Price09/2021
912310^100095-203693100095Patrick De Geest10/2022
912422779^22970-22970^22779100093Norbert Schneider08/2020
9125(2^332468+3130)/2100083Stefano Morozzi09/2020
9126(14*10^100075+61)/3100076Robert Price12/2018
9127(2^332435+3098)/2100073Stefano Morozzi09/2020
912828562^3189+3189^28562100072Hans Havermann05/2018
912910^100053+56193100054Alexander Weiss04/2024
91306^128565-127100044Lelio R Paula08/2016
9131(2^332317+2106)/2100038Stefano Morozzi09/2020
91332^332309-133100035Lelio R Paula02/2011
91342^332307+731100035Lelio R Paula07/2011
9132937^33662-33662^937100035Norbert Schneider05/2023
91352^332301+12927100033Lelio R Paula04/2013
913617025^23642-23642^17025100032Norbert Schneider04/2024
913723406^18781+18781^23406100031Hans Havermann04/2018
91382^332277-4573100026Yves Minet03/2019
913912^92684-13100023Lelio R Paula07/2016
914070^54207-54207^70100018Norbert Schneider04/2023
914178557*2^332193+55669100005Jorge Menendez04/2019
914278557*2^332192+72689100005Jorge Menendez04/2019
914310^100003+45799100004Stefano Morozzi04/2019
914410^100003+155461100004Stefano Morozzi04/2019
914510^100003+211389100004Stefano Morozzi04/2019
914610^100003+381027100004Stefano Morozzi04/2019
914710^100003+540703100004Stefano Morozzi04/2019
914810^100003+823977100004Stefano Morozzi04/2019
916010^100002+236023100003Stefano Morozzi05/2018
916110^100002+433741100003Stefano Morozzi05/2018
91492^332202+104659100003Stefano Morozzi04/2019
91502^332202+857539100003Stefano Morozzi04/2019
91512^332202+181773100003Stefano Morozzi04/2019
91522^332202+687543100003Stefano Morozzi04/2019
91532^332202+941595100003Stefano Morozzi04/2019
91542^332202+445813100003Stefano Morozzi04/2019
91552^332202+1599727100003Stefano Morozzi04/2019
91562^332202+1389567100003Stefano Morozzi04/2019
91572^332202+1206315100003Stefano Morozzi04/2019
91582^332202+1958647100003Stefano Morozzi04/2019
915910^100003-562857100003Patrick De Geest07/2019
9162(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
9163(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
916410^100002-249519100002Patrick De Geest07/2018
916510^100001+314199100002Patrick De Geest07/2018
921625206!+p(4114)100001Henri Lifchitz09/2005
921725206!-p(5447)100001Henri Lifchitz10/2005
921825206!-p(12402)100001Henri Lifchitz04/2006
921925206!-p(16290)100001Henri Lifchitz09/2006
922025206!-p(19647)100001Henri Lifchitz02/2007
92212^332194+11473100001Henri Lifchitz03/2007
921110^100000+342909100001Milton L. Brown12/2007
921210^100000+346579100001Robert Price04/2012
921310^100000+829767100001Robert Price05/2012
921410^100000+871899100001Robert Price05/2012
921510^100000+1475997100001Robert Price07/2012
920410^100000+1751769100001Robert Price08/2012
920510^100000+2155489100001Robert Price10/2012
920610^100000+2483527100001Robert Price12/2012
920710^100000+2503087100001Robert Price12/2012
920810^100000+2686179100001Robert Price12/2012
920910^100000+2688933100001Robert Price12/2012
921010^100000+3667159100001Robert Price08/2013
918510^100000+3938473100001Robert Price05/2015
918610^100000+3979761100001Robert Price05/2015
918710^100000+4293973100001Robert Price09/2015
918210^100000+4858267100001Robert Price12/2015
918310^100000+5113299100001Robert Price02/2016
918410^100000+5169411100001Robert Price02/2016
917410^100000+5354043100001Robert Price05/2016
917510^100000+5717979100001Robert Price05/2016
917610^100000+6080631100001Robert Price07/2016
917710^100000+6308469100001Robert Price07/2016
917810^100000+6512023100001Robert Price08/2016
917910^100000+6596557100001Robert Price08/2016
918010^100000+7115409100001Robert Price10/2016
918110^100000+7235803100001Robert Price10/2016
919110^100000+7867333100001Robert Price12/2016
919210^100000+8743093100001Robert Price02/2017
919310^100000+8955391100001Robert Price03/2017
919410^100000+9180019100001Robert Price03/2017
919510^100000+9225987100001Robert Price04/2017
919610^100000+9265587100001Robert Price04/2017
919710^100000+9287049100001Robert Price04/2017
919810^100000+9425053100001Robert Price05/2017
919910^100000+9450769100001Robert Price05/2017
920010^100000+9528747100001Robert Smith05/2017
920110^100000+9548071100001Robert Price06/2017
920210^100000+10064287100001Robert Price08/2017
920310^100000+10229569100001Robert Price10/2017
916610^100000+11187931100001Robert Price03/2018
916710^100000+11264721100001Robert Price04/2018
916810^100000+11477661100001Robert Price05/2018
916910^100000+11644653100001Robert Price07/2018
917010^100001-431439100001Patrick De Geest07/2018
917110^100000+11769399100001Robert Price08/2018
917210^100000+11848159100001Robert Price08/2018
917310^100000+11863467100001Robert Price08/2018
918810^100000+11992051100001Robert Price09/2018
91892^332196-1-2*29696100001Matt Stath11/2018
919010^100000+12363957100001Robert Price11/2018
92222^332196+1+2*17152100001Matt Stath12/2018
922310^100000+12778033100001Robert Price02/2019
922410^100000+13581679100001Robert Price05/2019
922510^100000+13613199100001Robert Price05/2019
922610^100000+13752327100001Robert Price05/2019
922710^100000+14139243100001Robert Price06/2019
922810^100000+14151057100001Robert Price06/2019
922910^100000+14218923100001Robert Price06/2019
923010^100000+24543147100001Robert Price08/2021
923110^100000+24781659100001Robert Price08/2021
923210^100000+24906153100001Robert Price08/2021
923310^100000+25682679100001Robert Price10/2021
923410^100000+25905301100001Robert Price10/2021
923510^100000+25923967100001Robert Price10/2021
923610^100000+26061691100001Robert Price10/2021
923710^100000+26173351100001Robert Price11/2021
923810^100000+26673487100001Robert Price11/2021
923910^100000+26849359100001Robert Price12/2021
924010^100000+26893887100001Robert Price12/2021
924110^100000+26954551100001Robert Price12/2021
924210^100000+27024543100001Robert Price12/2021
924310^100000+27060877100001Robert Price12/2021
924410^100000+27617577100001Robert Price03/2022
924510^100000+27869671100001Robert Price03/2022
924610^100000+27956481100001Robert Price03/2022
924710^100000+28078261100001Robert Price03/2022
924810^100000+28150203100001Robert Price03/2022
924910^100000+28626021100001Robert Price05/2022
925010^100000+28649299100001Robert Price05/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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